Question: Solve for $x$ and $y$ using elimination. ${-3x+4y = -14}$ ${3x+5y = 50}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. $9y = 36$ $\dfrac{9y}{{9}} = \dfrac{36}{{9}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-3x+4y = -14}\thinspace$ to find $x$ ${-3x + 4}{(4)}{= -14}$ $-3x+16 = -14$ $-3x+16{-16} = -14{-16}$ $-3x = -30$ $\dfrac{-3x}{{-3}} = \dfrac{-30}{{-3}}$ ${x = 10}$ You can also plug ${y = 4}$ into $\thinspace {3x+5y = 50}\thinspace$ and get the same answer for $x$ : ${3x + 5}{(4)}{= 50}$ ${x = 10}$